工作溫度對滾珠螺桿接觸應變及扭矩之影響

Effects of Temperature on The Contact Behavior and Preload Torque of Ball Screws

劉學棟(Tom-Hseuh-Tung Liu)

指導教授 ： 林派臣

國立中正大學/工學院/機械工程學系/碩士(2014年)

摘要

中文摘要
本文的目的是透過理論、數值及實驗方法研究工作溫度對雙螺帽滾珠螺桿的影響，包含滾珠/溝槽的接觸行為及螺桿的預壓扭矩。首先開發一座等效實驗平台，將螺桿中滾珠、螺桿及螺帽間複雜的接觸行為，轉換為簡單的軸向力接觸模型。運用數位影像相關法(Digital Image Correlation)量測不同溝槽牙型及軸向負載條件下，滾珠的應變場，並結合Hertz接觸理論對有限元素模型進行交互驗證。將驗證後的滾珠/溝槽有限元素模型，應用至2D及3D雙螺帽滾珠螺桿模型，取得不同溫度及不同偏移下的接觸應力數值解。接著，將理論模型加入溫度效應，取得不同溫度下滾珠/溝槽的接觸力理論解，再與數值解進行比較。最後製作一座雙螺帽滾珠螺桿平台，取得不同溫度下的預壓扭矩值。結果顯示，當偏移量越小，溫度變化對接觸壓力的影響越大。當偏移量相同及溫度上升時，接觸壓力及預壓扭矩皆呈線性下降，變化幅度以理論解最小，數值解其次，量測值最大。值得注意地，當溫度上升時，接觸壓力或接觸力下降的幅度不到扭矩量測值的十分之一，這顯示扭矩下降的主要原因不僅來自滾珠/溝槽的接觸行為，還有來自潤滑油黏滯係數的變化。
關鍵詞:滾珠螺桿，赫茲接觸，數位影像相關法，有限元素法，溫度

關鍵字

數位影像相關法 ； 赫茲接觸 ； 滾珠螺桿 ； 有限元素法 ； 溫度

並列摘要

Absract
In this paper, the effects of temperature on the roller-to-groove contact behavior and preload torque of double-nut ball screws were investigated. First, an equivalent platform was developed to transform the complex contact behavior between the ball, screw shaft, and screw nut to a simple axial-loaded contact model. Digital image correlation (DIC) technology was used to measure the strain fields of the roller under different groove shapes and axial loading conditions. The results and the Hertz contact theory were then used to validate the finite element contact models. After validation, 2D and 3D finite element models of double-nut ball screws were developed to obtain the contact pressures under different temperatures and offsets. Next, adding thermal expansion effect was used to obtain the contact forces under different temperatures. Finally, a double-nut ball screw platform was developed to obtain the pre-load torque under different temperatures. The results indicated that when the offset decreases, the effects of temperature on the contact press increase. When the temperature increases under identical offset, the contact pressure and pre-load torque decrease linearly. The order of change rate was the theoretical solutions, numerical solutions, and experimental solutions. Note that the change rate of contact pressure or load was only 1/10 of that of the pre-load torque. This indicated that the change of pre-load torque was probably caused by not only the contact behavior between grooves and balls but also the viscosity change of the lubricant inside the nut.

Keywords: ball screw, Hertz contact, digital image correlation, finite element method, temperature

並列關鍵字

finite element method ； digital image correlation ； Hertz contact ； ball screw ； temperature

參考文獻

[7] 朱元一, 2007, 歌德曲面與球面接觸變形之探討, 國立中興大學機械工程學系碩士論文

[2] K. Nakashima, K. Takafuji, Stiffness of a ball screw including the deformation of screw, nut and screw thread, (1st report, single nut), Transactions of the Japan Society of Mechanical Engineers, JSME, Part C, 54 (1987), pp. 2181-2187.

[3] J. F. Cuttino, T. A. Dow, B. F. Knight, Analytical and experimental identification of nonlinearities in a single-nut, preloaded ball screw, Journal of Mechanical Design, Transactions of the ASME, 119 (1997), pp. 15-19.

[4] H. T. Huang, B. Ravani, Contact stress analysis in ball screw mechanism using the tubular medical axis representation of contacting surfaces，Journal of Mechanical Design, Transactions of the ASME, 119 (1997), pp. 8-14.

[6] X.-S. Mei, M. Tsutsumi, T. Tao, N.-G. Sun, Study on the load distribution of ball screws with errors, Mechanism and Machine Theory, 38 (2003), p.p. 1257-1269.